We investigated a model of degenerate resource consumption in diverse populations placed in a stable homogenous environment. Analytical and cellular automata implementations of the model have been tested. The results suggest that degeneracy of a heritable phenotypic character – a preference for a particular kind of resource – leads to distributed competition for resource. This degeneracy-driven distributed competition facilitates either divergent dynamics or homogenous stasis, depending on the relative dispersions of trait degeneracy and resource distribution. The solutions are stable in the presence of limited environmental stochastic variability or heritable phenotypic variability. Importantly, the observed behaviors – either heritable phenotypic divergence or stasis – did not change the overall adaptation of the population in that they did not affect the total population size or the overall efficiency of resource consumption.
Such a role of degeneracy in population dynamics was not initially predicted in the early works that were concerned with the contributions of degeneracy to reliability in stable environments and adaptability to novel environments [28, 29]. In teleological terms, the “purpose” of degeneracy is to increase fitness. In a stable environment, degeneracy ensures the ability of a population – of individuals, cells, or molecules – to withstand a significant structural loss without a long-lasting functional defect. Such robustness is possible, because, in a system composed of degenerate units, the function of the damaged or lost elements is taken over, due to functional degeneracy, by the remaining elements. Such degeneracy-dependent robustness is critical for survival in familiar environments [28, 29]. Arguably, without degeneracy, trait diversity alone would not be able to safeguard the survival of populations following drastic changes in the environment: all current populations have been shaped by past natural selection, which leaves populations unprepared for novel environmental challenges. No matter how diverse a population, the diversity of novel environmental features is larger, and survival due to an increase in diversity alone cannot be ensured. In addition to trait diversity, degeneracy is needed, because it drastically increases the spectrum of possible adaptive responses to novelty [28, 29]. The degeneracy-driven dynamics observed in our model have no direct adaptive benefits to a population as a whole. Indeed, in a stable, homogenous environment represented by uniform resource distribution, the shape of the population distribution varies without affecting overall fitness. As such, the observed “patterning” of populations is an “unintended” (using the same teleological terminology) consequence of degeneracy. Nevertheless, the observed dynamics would contribute to both divergent evolution and static homogeneity in populations.
There are several implications to these findings. One, these results add specifics and significantly expand Darwin’s explanations to the difficult question, “why do species exist?” By considering the contribution of degeneracy-driven competition, we add important details to Darwin’s argument for the role of intra- and inter-population rivalry in suppression and, ultimately, exclusion of intermediate forms. Two, our results suggest that the same mechanism plays a key role not only in the emergence of diversification, but also in maintaining population stasis. In both cases, an environmental change is not required, and the population behavior – either divergence or stasis – is defined solely by degeneracy in relation to the overall environment. Three, these findings suggest that observed rapid (in evolutionary terms) transitions between prolonged evolutionary stasis and rapid diversification [1–8, 10, 11] are due to the overall (non-local) broadening or narrowing of resource distribution, leading to diversification or stasis, respectively.
An important limitation is that only asexual reproduction has been modeled, as the “offspring” are exact copies (except the version with phenotypic variability as shown in Figure 8) of the “parent” (based on their identical location in the model space). This is, in part, a result of the reductionist nature of this model and, in part, a consequence of heritable phenotypes rather than genotypes being considered. Phenotypes but not genotypes are the primary substrate of selection, and we needed to avoid the considerable complexities associated with variable genotype–phenotype mappings [48–50], which is a topic beyond the scope of the current work. Furthermore, investigating the effects of sexual reproduction in degenerate repertoires will require a separate investigation, owing to the need to assess the contributions of complete and incomplete dominance, co-dominance, and epistasis, not only on median trait values but also on degeneracy itself, as the latter may vary among individuals. Clearly, our model does not consider hybrid speciation, and it can be readily envisioned that heterospecific mating would abrogate the observed patterning of model populations. Exchange of genes between organisms belonging to divergent lineages and thus leading to “reticulate evolution” has been well documented [51, 52]. Even less remote (conspecific) crosses between phenotypically distant individuals (negative assortative mating) might significantly attenuate the model dynamics. Therefore, the effects of sexual reproduction will be studied in our future work.
Nevertheless, it can be argued that the results of this modeling, particularly the version with phenotypic variability (Figure 8), may be relevant not only to asexual but also, in part, to sexual reproduction. Our findings remain relevant to reproductive isolation leading to conspecific crosses between phenotypically similar individuals in sexual species. Reproductive isolation occurs through behavioral (trait-based positive assortative mating), morphological, physiological, or biochemical mechanisms. The research literature abounds with evidence of reproductive isolation, including positive assortative mating (reviewed [53, 54]). It can be argued that in these cases, the crosses are rather similar to the parents, as mate selection occurs from a pool of similar individuals. Even with some randomness in mate selection from the restricted pool, and the subsequent limited stochasticity in the heritable phenotypes of offspring, the overall model dynamics remain preserved, as demonstrated in Figure 8 and described in Results.
Furthermore, recent findings  suggest that limited heterospecific hybridization may be also relevant to the results of our model, particularly those in Figure 8. Neotropical primates Alouatta palliata and A. pigra, which diverged from a shared progenitor about 3 mya, are mostly allopatric, except for a small sympatric area of contact in which they interbreed. In this contact area, purebred individuals coexist with first-generation, backcrossed, and multigenerational hybrids. Assessing morphological variation of genetically confirmed hybrids, the researchers found that “multigenerational backcrossed hybrids resemble the parental species with which they share most of their alleles.” In contrast, “intermediate hybrids exhibited great variation in morphology,” but such intermediates comprised only ~12% of the individuals in the hybrid zone. The researchers concluded that “morphology may not always be a reliable indicator of hybrid status” and that “hybrid zones could comprise a large number of multigenerational backcrossed hybrids that are indistinguishable from the parental species” . These observations are in agreement with our modeling approach, which is based on phenotypes (representing morphology in ) but not genotypes (representing genetic characteristics in ); this approach is relevant, because natural selection acts on phenotypes and not genotypes. The authors  discuss numerous other examples of cryptic hybridization, where molecular methods identified hybrid individuals that could not be distinguished morphologically from the parental species. Importantly for our modeling results, not only were the majority of hybrids phenotypically indistinguishable from the parental species but the remaining minority of hybrids were phenotypically variable, as modeled in the case represented by Figure 8. Thus, our model is relevant not only to asexual but also to conspecific and even heterospecific sexual reproduction.
The model has other limitations, and additional work is needed to more fully understand the nature of degeneracy-driven dynamics in populations. A one-dimensional – considering only a single heritable phenotypic trait – model has been considered here. Realistic degenerate units are multi-dimensional and characterized by numerous traits; these traits may also interact in a pair-wise or more complex fashion. The results of this work are purely theoretical and computational, and will need to be confirmed with experimental and observational evidence. Experimenting with degeneracy may be challenging, as general practical approaches have not yet been elaborated, and quantitative measures of degeneracy are yet to be defined. Various resource distributions, static and dynamic or uniform and non-uniform, need to be assessed for their effects on population changes in order to better approximate real-world resources. Populations with mixed, heritably retained degeneracy ranges (narrow, intermediate, and broad) need to be tested to better approximate real-world populations. As a theoretical exercise and in preparation for the degeneracy-driven technologies of the future , it would be interesting to assess the possibility that individual degeneracy ranges vary in time, stochastically or depending on current fitness. In the implementation presented in the current study, trait degeneracy was intrinsic to individuals and had no cost to them, whereas in some realistic populations, broader degeneracy may come at a higher individual or systemic cost, and must be considered as explorative behavior. For example, humoral adaptive immunity invests in diversity and degeneracy of the B cell repertoire through somatic mutagenesis. The effect of the cost of degeneracy on population dynamics needs to be studied. Even with these simplifications, the model shows interesting behavior, offering new insight into the dynamics of degenerate repertoires. Specifically, trait degeneracy is shown to be a driving factor of both static homogeneity and dynamic divergence in populations.